Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three-cottage problem. More important applications can be found in printing electronic circuits where the aim is to print (embed) a circuit (the graph) on a circuit board (the surface) without two connections crossing each other and resulting in a short circuit.
Graphs as topological spaces
An undirected graph can be viewed as an abstract simplicial complexC with a single-element set per vertex and a two-element set per edge. The geometric realization |C| of the complex consists of a copy of the unit interval [0,1] per edge, with the endpoints of these intervals glued together at vertices. In this view, embeddings of graphs into a surface or as subdivisions of other graphs are both instances of topological embedding, homeomorphism of graphs is just the specialization of topological homeomorphism, the notion of a connected graph coincides with topological connectedness, and a connected graph is a tree if and only if its fundamental group is trivial.
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see Graph (discrete mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.
Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.
Graph
In the most common sense of the term, a graph is an ordered pairG = (V, E) comprising a setV of vertices or nodes or points together with a set E of edges or arcs or lines, which are 2-element subsets of V (i.e. an edge is related with two vertices, and the relation is represented as an unordered pair of the vertices with respect to the particular edge). To avoid ambiguity, this type of graph may be described precisely as undirected and simple.
In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and the edges by Jordan arcs (connected pieces of Jordan curves) joining the corresponding pairs of points. The points representing the vertices of a graph and the arcs representing its edges are called the vertices and the edges of the topological graph.
It is usually assumed that any two edges of a topological graph cross a finite number of times,
no edge passes through a vertex different from its endpoints, and no two edges touch each other
(without crossing). A topological graph is also called a drawing of a graph.
An important special class of topological graphs is the class of geometric graphs, where
the edges are represented by line segments. (The term geometric graph is sometimes used in a broader, somewhat vague sense.)
The theory of topological graphs is an area of graph theory, mainly concerned with combinatorial properties of topological graphs, in particular, with the crossing patterns of their edges. It is closely related to graph drawing, a field which is more application oriented, and topological graph theory, which focuses on embeddings of graphs in surfaces (that is, drawings without crossings).
My previous video on Depth-First Search https://youtu.be/5GcSvYDgiSo
This video should give you a quick overview of Topological Sort.
The animations are made with my tool Alvis.
Play with the demo here https://alvis-algorithms.web.app/?a=tsrt
View the GitHub repository here https://github.com/carltheperson/alvis
Feel free to leave a comment if you find a mistake. You can also open an issue on GitHub.
Thanks for watching!
published: 15 Jan 2022
Topological Sort Algorithm | Graph Theory
How to find the topological sort of a directed acyclic graph
Shortest path on a Directed Acyclic Graph (DAG):
https://www.youtube.com/watch?v=TXkDpqjDMHA
Github source code link:
https://github.com/williamfiset/algorithms#graph-theory
0:00 Intro
0:18 Topological sort real life examples
2:49 Technical definition of topsort
3:42 The need for directed acyclic graphs
4:46 Topological ordering of trees
5:26 Topological sort algorithm
9:28 Topological sort source code
==================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resou...
published: 19 Oct 2017
Topological Sorting | GeeksforGeeks
Explanation for the article: http://www.geeksforgeeks.org/topological-sorting/
This video is contributed by Illuminati.
published: 22 Oct 2016
6.10 Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
In today's Video I have explained Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
DSA Full Course: https: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bbKJzrsKfMpo_grxuLl8LU
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Python Full Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bZSiqiOL5ta39vSnBxpOPT
Printing Pattern in C: https://www.youtube.com/playlist?list=PLdo5W4Nhv31Yu1igxTE2x0aeShbKtVcCy
DAA Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31ZTn2P9vF02bkb3SC8uiUUn
Placement Series: https://www.youtube.com/playlist?list=P...
published: 03 Feb 2019
Topological Sort Graph Algorithm
Generate topologically sorted order for directed acyclic graph.
https://www.facebook.com/tusharroy25
https://github.com/mission-peace/interview/blob/master/src/com/interview/graph/TopologicalSort.java
https://github.com/mission-peace/interview/wiki
published: 03 Aug 2015
Topological Sorting with examples | Topological Sorting using DFS | Imp For Placements & Comp. Exams
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published: 12 Sep 2022
G-21. Topological Sort Algorithm | DFS
GfG-Problem Link: https://bit.ly/3PvBfsm
C++/Java/Codes and Notes Link: https://takeuforward.org/data-structure/topological-sort-algorithm-dfs-g-21/
DP Series: https://www.youtube.com/watch?v=FfXoiwwnxFw&list=PLgUwDviBIf0qUlt5H_kiKYaNSqJ81PMMY
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published: 05 Sep 2022
Lecture # 1 Introduction to Graph Theory (Network Topology)
In this video, Introduction of Graph theory is presented and its terminologies are discussed.
published: 31 Mar 2019
Topological Ordering of Graphs
An introduction to Directed Acyclic Graphs and the algorithm to produce topological orderings of such graphs.
published: 17 Mar 2021
Topological Sort | Kahn's Algorithm | Graph Theory
Source code repository:
https://github.com/williamfiset/algorithms#graph-theory
Video slides:
https://github.com/williamfiset/algorithms/tree/master/slides
Website:
http://www.williamfiset.com
Audio intro/outro composed by Richard Saney ([email protected])
0:00 Intro
0:22 Topological sort example
2:09 Topological sort motivation
2:37 Topological ordering
3:36 Directed acyclic graphs
4:31 A case against cycles
5:36 Kahn's algorithm intuition
6:05 Kahn's algorithm example1
7:11 Kahn's algorithm example2
11:15 Kahn's algorithm pseudocode
12:57 Outro
===================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired...
My previous video on Depth-First Search https://youtu.be/5GcSvYDgiSo
This video should give you a quick overview of Topological Sort.
The animations are made ...
My previous video on Depth-First Search https://youtu.be/5GcSvYDgiSo
This video should give you a quick overview of Topological Sort.
The animations are made with my tool Alvis.
Play with the demo here https://alvis-algorithms.web.app/?a=tsrt
View the GitHub repository here https://github.com/carltheperson/alvis
Feel free to leave a comment if you find a mistake. You can also open an issue on GitHub.
Thanks for watching!
My previous video on Depth-First Search https://youtu.be/5GcSvYDgiSo
This video should give you a quick overview of Topological Sort.
The animations are made with my tool Alvis.
Play with the demo here https://alvis-algorithms.web.app/?a=tsrt
View the GitHub repository here https://github.com/carltheperson/alvis
Feel free to leave a comment if you find a mistake. You can also open an issue on GitHub.
Thanks for watching!
How to find the topological sort of a directed acyclic graph
Shortest path on a Directed Acyclic Graph (DAG):
https://www.youtube.com/watch?v=TXkDpqjDMHA
Gith...
How to find the topological sort of a directed acyclic graph
Shortest path on a Directed Acyclic Graph (DAG):
https://www.youtube.com/watch?v=TXkDpqjDMHA
Github source code link:
https://github.com/williamfiset/algorithms#graph-theory
0:00 Intro
0:18 Topological sort real life examples
2:49 Technical definition of topsort
3:42 The need for directed acyclic graphs
4:46 Topological ordering of trees
5:26 Topological sort algorithm
9:28 Topological sort source code
==================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube:
https://www.udemy.com/course/graph-theory-algorithms
How to find the topological sort of a directed acyclic graph
Shortest path on a Directed Acyclic Graph (DAG):
https://www.youtube.com/watch?v=TXkDpqjDMHA
Github source code link:
https://github.com/williamfiset/algorithms#graph-theory
0:00 Intro
0:18 Topological sort real life examples
2:49 Technical definition of topsort
3:42 The need for directed acyclic graphs
4:46 Topological ordering of trees
5:26 Topological sort algorithm
9:28 Topological sort source code
==================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube:
https://www.udemy.com/course/graph-theory-algorithms
In today's Video I have explained Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
DSA Full Course: https: https://www.yo...
In today's Video I have explained Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
DSA Full Course: https: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bbKJzrsKfMpo_grxuLl8LU
******************************************
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C Programming Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31a8UcMN9-35ghv8qyFWD9_S
C++ Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YU5Wx1dopka58teWP9aCee
Python Full Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bZSiqiOL5ta39vSnBxpOPT
Printing Pattern in C: https://www.youtube.com/playlist?list=PLdo5W4Nhv31Yu1igxTE2x0aeShbKtVcCy
DAA Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31ZTn2P9vF02bkb3SC8uiUUn
Placement Series: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YvlDpJhvOYbM9Ap8UypgEy
Dynamic Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31aBrJE1WS4MR9LRfbmZrAQu
Operating Systems: //www.youtube.com/playlist?list=PLdo5W4Nhv31a5ucW_S1K3-x6ztBRD-PNa
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In today's Video I have explained Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
DSA Full Course: https: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bbKJzrsKfMpo_grxuLl8LU
******************************************
More Playlists:
C Programming Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31a8UcMN9-35ghv8qyFWD9_S
C++ Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YU5Wx1dopka58teWP9aCee
Python Full Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31bZSiqiOL5ta39vSnBxpOPT
Printing Pattern in C: https://www.youtube.com/playlist?list=PLdo5W4Nhv31Yu1igxTE2x0aeShbKtVcCy
DAA Course: https://www.youtube.com/playlist?list=PLdo5W4Nhv31ZTn2P9vF02bkb3SC8uiUUn
Placement Series: https://www.youtube.com/playlist?list=PLdo5W4Nhv31YvlDpJhvOYbM9Ap8UypgEy
Dynamic Programming: https://www.youtube.com/playlist?list=PLdo5W4Nhv31aBrJE1WS4MR9LRfbmZrAQu
Operating Systems: //www.youtube.com/playlist?list=PLdo5W4Nhv31a5ucW_S1K3-x6ztBRD-PNa
DBMS: https://www.youtube.com/playlist?list=PLdo5W4Nhv31b33kF46f9aFjoJPOkdlsRc
***********************************************
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Generate topologically sorted order for directed acyclic graph.
https://www.facebook.com/tusharroy25
https://github.com/mission-peace/interview/blob/master/src...
Generate topologically sorted order for directed acyclic graph.
https://www.facebook.com/tusharroy25
https://github.com/mission-peace/interview/blob/master/src/com/interview/graph/TopologicalSort.java
https://github.com/mission-peace/interview/wiki
👉Subscribe to our new channel:https://www.youtube.com/@varunainashots
►Design and Analysis of algorithms (DAA) (Complete Playlist):
https://www.youtube.com/pl...
👉Subscribe to our new channel:https://www.youtube.com/@varunainashots
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►Database Management System:
https://www.youtube.com/playlist?list=PLxCzCOWd7aiFAN6I8CuViBuCdJgiOkT2Y
► Theory of Computation
https://www.youtube.com/playlist?list=PLxCzCOWd7aiFM9Lj5G9G_76adtyb4ef7i
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Source code repository:
https://github.com/williamfiset/algorithms#graph-theory
Video slides:
https://github.com/williamfiset/algorithms/tree/master/slides
We...
Source code repository:
https://github.com/williamfiset/algorithms#graph-theory
Video slides:
https://github.com/williamfiset/algorithms/tree/master/slides
Website:
http://www.williamfiset.com
Audio intro/outro composed by Richard Saney ([email protected])
0:00 Intro
0:22 Topological sort example
2:09 Topological sort motivation
2:37 Topological ordering
3:36 Directed acyclic graphs
4:31 A case against cycles
5:36 Kahn's algorithm intuition
6:05 Kahn's algorithm example1
7:11 Kahn's algorithm example2
11:15 Kahn's algorithm pseudocode
12:57 Outro
===================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
Source code repository:
https://github.com/williamfiset/algorithms#graph-theory
Video slides:
https://github.com/williamfiset/algorithms/tree/master/slides
Website:
http://www.williamfiset.com
Audio intro/outro composed by Richard Saney ([email protected])
0:00 Intro
0:22 Topological sort example
2:09 Topological sort motivation
2:37 Topological ordering
3:36 Directed acyclic graphs
4:31 A case against cycles
5:36 Kahn's algorithm intuition
6:05 Kahn's algorithm example1
7:11 Kahn's algorithm example2
11:15 Kahn's algorithm pseudocode
12:57 Outro
===================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
My previous video on Depth-First Search https://youtu.be/5GcSvYDgiSo
This video should give you a quick overview of Topological Sort.
The animations are made with my tool Alvis.
Play with the demo here https://alvis-algorithms.web.app/?a=tsrt
View the GitHub repository here https://github.com/carltheperson/alvis
Feel free to leave a comment if you find a mistake. You can also open an issue on GitHub.
Thanks for watching!
How to find the topological sort of a directed acyclic graph
Shortest path on a Directed Acyclic Graph (DAG):
https://www.youtube.com/watch?v=TXkDpqjDMHA
Github source code link:
https://github.com/williamfiset/algorithms#graph-theory
0:00 Intro
0:18 Topological sort real life examples
2:49 Technical definition of topsort
3:42 The need for directed acyclic graphs
4:46 Topological ordering of trees
5:26 Topological sort algorithm
9:28 Topological sort source code
==================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube:
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In today's Video I have explained Topological Sorting (with Examples) | How to find all Topological Orderings of a Graph
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Source code repository:
https://github.com/williamfiset/algorithms#graph-theory
Video slides:
https://github.com/williamfiset/algorithms/tree/master/slides
Website:
http://www.williamfiset.com
Audio intro/outro composed by Richard Saney ([email protected])
0:00 Intro
0:22 Topological sort example
2:09 Topological sort motivation
2:37 Topological ordering
3:36 Directed acyclic graphs
4:31 A case against cycles
5:36 Kahn's algorithm intuition
6:05 Kahn's algorithm example1
7:11 Kahn's algorithm example2
11:15 Kahn's algorithm pseudocode
12:57 Outro
===================================
Practicing for interviews? I have used, and recommend `Cracking the Coding Interview` which got me a job at Google. Link on Amazon: https://amzn.to/3cvMof5
A lot of the content on this channel is inspired by the book `Competitive Programming` by Steven Halim which I frequently use as a resource and reference. Link on Amazon: https://amzn.to/3wC2nix
Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three-cottage problem. More important applications can be found in printing electronic circuits where the aim is to print (embed) a circuit (the graph) on a circuit board (the surface) without two connections crossing each other and resulting in a short circuit.
Graphs as topological spaces
An undirected graph can be viewed as an abstract simplicial complexC with a single-element set per vertex and a two-element set per edge. The geometric realization |C| of the complex consists of a copy of the unit interval [0,1] per edge, with the endpoints of these intervals glued together at vertices. In this view, embeddings of graphs into a surface or as subdivisions of other graphs are both instances of topological embedding, homeomorphism of graphs is just the specialization of topological homeomorphism, the notion of a connected graph coincides with topological connectedness, and a connected graph is a tree if and only if its fundamental group is trivial.
At 1 p.m. on Friday, Feb ... Events will take place across campus from 9 a.m ... 25. Finally, students in the Mathematical PuzzleProgram will engage in problem solving puzzles created using design theory, game theory, number theory, graph theory and topology.